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Monday, December 12, 2011
Ryan Braun and Bayes
Let’s say that the chances of a false positive for the Braun test is 1 in a 1000. What are the chances that Braun took a banned substance and that he did NOT have a false positive?
On the flip side, sort of, our friend Richard Justice (Houston sports journalist and radio guy) said that he believed Braun (that he did not take anything and it must have been a mistake of some sort). When asked why, he said the usual - Braun is a stand-up, honest, smart guy, etc.
So Justice (unbeknownst to him apparently) was simply stating the anterior or prior probability - that Braun is not a likely candidate for being a PED user. But, we have more information of course. We have a posterior probability that he took a banned substance, which is the 1 minus the probability of a false positive or some other sort of “mistake.”
So, again, given the prior and the posterior, what are the chances that Braun cheated?
And Justice, among others, needs a lesson about Bayesian math…